Abstract
A typical space structure is composed of piece-wise periodic arrays of connected truss units. These arrays can intersect each other, and form multiple closed loops. In this paper, a detailed step-by-step numerical procedure is provided for computing the response of such a structure to external excitations. The basic idea is to treat an array of connected truss units as a multi-channel waveguide, capable of transmitting several types of wave motions. Each waveguide, or each junction where several waveguides intersect, can be characterized by a wave scattering matrix, which is composed of the transmission and reflection submatrices. A reflection submatrix reverses the direction of incoming waves, whereas a transmission submatrix permits the incoming waves to enter, or to be directed to other waveguides. By use of wave scattering matrices in the formulation, the numerical computation always follows the directions of propagation of various waves. Thus, numerical stability is assured, since the amplitude of wave motion decays as it propagates along a path due to structural damping. The numerical procedure described herein represents an extension of the author's previous works by (1) describing, for the first time, the dynamics of individual truss arrays in terms of scattering matrices, (2) adopting a new bookkeeping system to accommodate more complicated configurations of structural networks, and (3) developing an efficient procedure to eliminate step-by-step superfluous unknowns, thus simplifying the calculation. Combination of the three advances makes it possible to treat, for the first time, such complicated configurations as multiple closed loops. Since the actual truss-type construction is retained when obtaining the wave scattering matrices, the procedure is considered more accurate than those based on substitution for truss construction of Timoshenko beam elements. Application of the procedure is illustrated by an example.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
